I was not attempting to define the term, I was explaining it's practical impact in an accessible way.

"and it is important to add the rest:

giving the appearance of CBM having been used, but without turning the body."

No, THAT is where you start confusing people.

Practically speaking, when a step is described as in CBMP, it means that it is placed diagonally across your body to the other side.

The other paramaters of the step description will tell you if you should, or should not be rotating.

And the reason it is important to treat those seperately is that your insistence on using the formal definition would lead one to believe that CBMP and rotating cannot coincide when in fact they can. Then we have to explain that the coinciding rotation must not be the source of the CBMP. And we get into arguments with quite established teachers who never managed to understand that particular aspect of the formal definition.

Which is why I revert the the practical explanation, NOT the formal definition, because it is something that should be approachable by all dancers from the start: